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3 years ago

Find the value of x for which (2)^3x = 8^2.

Mathematics

1 answer:

vredina [299]3 years ago

5 0

Answer:

x = 2

Step-by-step explanation:

Using the rule of exponents

$(a^m)^{n}$ = $a^{mn}$

$(2)^{3x}$ = $2^{3x}$ and 8 = (2³ )² = $2^{6}$ , so

$2^{3x}$ = $2^{6}$

Since the bases on both sides are equal, both 2, equate the exponents

3x = 6 ( divide both sides by 3 )

x = 2

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Solve for x. any help would be appreciated thanks

WARRIOR [948]

The correct answer is x=5

8 0

3 years ago

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2 to the power of 6 divided by 2?

umka21 [38]

The answer is 64
2x2=4
4x2=8
8x2=16
16x2=36
36x2=64
64x2=128
128 divided by 2
64

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3 years ago

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Which statements are TRUE? Select all that apply. Marisa drives 112 miles in 1 hour and 45 minutes, which means her speed is 64

valentinak56 [21]

Answer: See explanation

Step-by-step explanation:

a. Marisa drives 112 miles in 1 hour and 45 minutes, which means her speed is 64 miles per hour.

Speed = Distance / Time

= 112 / 1 45/60

= 112 / 1 3/4

= 112 × 4/7

= 64 miles per hour.

TRUE

b . If 6 pens cost $7.74, then 7 pens cost $9.03.

Cost of one pen = $7.74/6 = $1.29

Cost of 7 pens = $1.29 × 7 = $9.03

TRUE

c. If Raymond drives at a speed of 57 miles per hour, then it takes him 4 hours and 10 minutes to drive 256.5 miles.

Speed = Distance / Time

Speed = 256.5 / 57 = 4.5 = 4 hours 30 minutes

FALSE

d. If 17 identical cans of soup cost $38.59, then 3 of the cans must cost $6.81.

Cost of one can = $38.59 / 17 = $2.27

Cost of 3 cans = $2.27 × 3 = $6.81

TRUE

e. Mr. Mayes buys two dozen eggs for $8.40, which means that he pays 70 cents per egg.

A dozen = 12

2 dozens = 12 × 2 = 24

Cost of one egg = $8.40 / 24 = 0.35 = 35 cents

FALSE

8 0

3 years ago

The yearly cost in dollars, y, at a video game arcade based on total game tokens purchased, x, is y = x + 60 for a member and y

morpeh [17]

We have the yearly cost in dollars y at a video game arcade based on total game tokens purchased $x$ . So we know that:

 $y=x+60:\ equation \ for \ a \ member$ 

 $y=x:\ equation \ for \ a \ nonmember$ 

Then we can study this problem by using the graph in the figure below. We know that if there's no any purchase, the yearly cost for a member will be $60 and for a nonmember there will not be any cost. From this, we can affirm that the cost of membership is equal to $60.

On the other hand, both members and nonmembers will pay the same price on the total game tokens purchased, this is true because of the same slope that members and nonmembers have in the equations.